Non-linear hyperbolic equations in domains with conical points: existence and regularity of solutions
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | German |
| Published: |
Berlin
Akad.-Verl.
1995
|
| Edition: | 1. ed. |
| Series: | Mathematical research
84 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 230 S. |
| ISBN: | 3055016912 |
Staff View
MARC
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| 100 | 1 | |a Witt, Ingo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Non-linear hyperbolic equations in domains with conical points |b existence and regularity of solutions |c Ingo Witt |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Berlin |b Akad.-Verl. |c 1995 | |
| 300 | |a 230 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematical research |v 84 | |
| 502 | |a Teilw. zugl.: Bonn, Univ., Diss. | ||
| 650 | 7 | |a Equations d'évolution - Théorie asymptotique |2 ram | |
| 650 | 7 | |a Equations différentielles hyperboliques - Solutions numériques |2 ram | |
| 650 | 4 | |a Differential equations, Hyperbolic |x Numerical solutions | |
| 650 | 4 | |a Evolution equations |x Asymptotic theory | |
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Record in the Search Index
| _version_ | 1804124705990377472 |
|---|---|
| adam_text | Contents
Introduction H
1 Formulation of the problem 11
1.1 Linear equations 11
1.2 Quasi linear equations 15
1.3 Open problems 18
2 Notation and function spaces 19
2.1 Function spaces on piece wise smooth domains 19
2.2 Weighted totally characteristic Sobolev spaces 20
1 Abstract Linear Hyperbolic Equations 27
1.1 Existence of weak solutions. CD systems 28
1.1.1 Function and operator spaces I 28
1.1.2 CD systems 30
1.1.3 The existence theorem 31
1.2 Higher regularity in scales of Frechet spaces 32
1.2.1 Function and operator spaces II 32
1.2.2 Assumptions for the regularity theorem 37
1.2.3 Compatibility conditions 39
1.2.4 Kato s reduction 40
1.2.5 The regularity theorem 41
1.3 Energy estimates 42
1.4 Equations of second order 48
8 Contents
1.4.1 CD systems of second order 48
1.4.2 Stability for second order systems 49
1.4.3 Linear wave equations with Dirichlet boundary condition 52
1.4.4 Higher regularity for equations of second order 53
1.4.5 Application to linear wave equations with C°° coefficients 56
1.4.6 Appendix to 1.4.5 : Regularity for linear elliptic problems 58
2 Linear Hyperbolic Equations in Domains with Conical Points 59
2.1 Linear hyperbolic equations with non smooth coefficients in do¬
mains with conical points 60
2.1.1 The double scale and assumptions on the coefficients . . 61
2.1.2 Elliptic differential operators with C°° coefficients in do¬
mains with conical singularities 62
2.1.3 Fredholm properties and elliptic regularity in case of non
smooth coefficients 64
2.1.4 Existence and higher regularity of solutions to linear hy¬
perbolic equations in domains with conical points .... 69
2.2 Branching behaviour of discrete asymptotics of solutions to
linear hyperbolic equations with C°° coefficients near conical
points 73
2.3 The leading asymptotic term of solutions to linear hyperbolic
differential equations in case of non smooth coefficients 76
2.3.1 The leading asymptotic term in case of non smooth co¬
efficients at a fixed time 76
2.3.2 The branching behaviour of the leading asymptotic term
in case of non smooth coefficients 82
3 Quasi Linear Hyperbolic Equations in Domains with Conical
Points 85
3.1 Assumptions and compatibility conditions 86
3.1.1 Abstract formulation of the problem 87
3.1.2 The condition (QQla) 88
3.1.3 Some technical lemmata 89
Contents 9
3.1.4 Assumptions on the coefficients 98
3.1.5 Compatibility conditions of order s 99
3.2 Infinitely many compatibility conditions 100
3.2.1 The spaces Ta(I) 101
3.2.2 The condition (QQlb) 103
3.2.3 The conditions (QQ2) (QQ4) 105
3.2.4 A further condition 108
3.2.5 The condition (QQ5) Ill
3.2.6 The linearized equations 113
3.2.7 The fixed point argument 115
3.3 Finitely many compatibility conditions 118
3.3.1 Approximation of the initial data by initial data satisfy¬
ing infinitely many compatibility conditions 119
3.3.2 Approximation by solutions that belong to C°°([0,T];
Uoo 1(n)r h1*(n)) 129
4 Pseudo Differential Operators with Non Smooth Symbols
on Manifolds with Conical Singularities 133
4.1 Pseudo differential operators on manifolds with conical singu¬
larities 134
4.1.1 Mellin pseudo differential operators 134
4.1.2 The algebra C(X,fl*) 151
4.1.3 Further comments and remarks 157
4.2 Pseudo differential operators having symbols with limited
smoothness 164
4.2.1 Operators on R 165
4.2.2 The operator classes A™cl(X) 177
4.2.3 Further comments 179
4.3 Pseudo differential operators with non smooth symbols on man¬
ifolds with conical singularities 181
4.3.1 Background and notation 182
10 Contents
4.3.2 The non smooth cone calculus with continuous asymp
totics 186
4.3.3 The non smooth cone calculus with discrete asymptotics 193
4.4 The branching behaviour of discrete asymptotics of solutions to
linear hyperbolic equations near conical points 195
4.4.1 Analytic functional 197
4.4.2 Function spaces with branching discrete asymptotics . . 200
4.4.3 Families of operators with branching discrete asymptot¬
ics 203
4.4.4 The asymptotics of solutions near conical singularities . 206
4.4.5 Remarks on the case of operators with non smooth coef¬
ficients 212
A An Energy Method for Quasi Linear Hyperbolic Equations
of Special Kind in Two Dimensional Domains with Conical
Singularities 215
A. 1 An abstract energy method for quasi linear hyperbolic evolution
equations of second order 216
A.1.1 Linear equations 216
A.1.2 Quasi linear equations 220
A.2 Application to special quasi linear hyperbolic evolution equa¬
tions in two dimensional domains with conical singularities . . 223
Bibliography 227
|
| any_adam_object | 1 |
| author | Witt, Ingo |
| author_facet | Witt, Ingo |
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| ctrlnum | (OCoLC)33125094 (DE-599)BVBBV010288811 |
| dewey-full | 515.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.35 |
| dewey-search | 515.35 |
| dewey-sort | 3515.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Thesis Book |
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| id | DE-604.BV010288811 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:49:55Z |
| institution | BVB |
| isbn | 3055016912 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006845435 |
| oclc_num | 33125094 |
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| physical | 230 S. |
| publishDate | 1995 |
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| publisher | Akad.-Verl. |
| record_format | marc |
| series | Mathematical research |
| series2 | Mathematical research |
| spelling | Witt, Ingo Verfasser aut Non-linear hyperbolic equations in domains with conical points existence and regularity of solutions Ingo Witt 1. ed. Berlin Akad.-Verl. 1995 230 S. txt rdacontent n rdamedia nc rdacarrier Mathematical research 84 Teilw. zugl.: Bonn, Univ., Diss. Equations d'évolution - Théorie asymptotique ram Equations différentielles hyperboliques - Solutions numériques ram Differential equations, Hyperbolic Numerical solutions Evolution equations Asymptotic theory Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd rswk-swf Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Nichtlineare Evolutionsgleichung (DE-588)4221363-0 s Hyperbolische Differentialgleichung (DE-588)4131213-2 s DE-604 Mathematical research 84 (DE-604)BV000008585 84 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006845435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Witt, Ingo Non-linear hyperbolic equations in domains with conical points existence and regularity of solutions Mathematical research Equations d'évolution - Théorie asymptotique ram Equations différentielles hyperboliques - Solutions numériques ram Differential equations, Hyperbolic Numerical solutions Evolution equations Asymptotic theory Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| subject_GND | (DE-588)4221363-0 (DE-588)4131213-2 (DE-588)4113937-9 |
| title | Non-linear hyperbolic equations in domains with conical points existence and regularity of solutions |
| title_auth | Non-linear hyperbolic equations in domains with conical points existence and regularity of solutions |
| title_exact_search | Non-linear hyperbolic equations in domains with conical points existence and regularity of solutions |
| title_full | Non-linear hyperbolic equations in domains with conical points existence and regularity of solutions Ingo Witt |
| title_fullStr | Non-linear hyperbolic equations in domains with conical points existence and regularity of solutions Ingo Witt |
| title_full_unstemmed | Non-linear hyperbolic equations in domains with conical points existence and regularity of solutions Ingo Witt |
| title_short | Non-linear hyperbolic equations in domains with conical points |
| title_sort | non linear hyperbolic equations in domains with conical points existence and regularity of solutions |
| title_sub | existence and regularity of solutions |
| topic | Equations d'évolution - Théorie asymptotique ram Equations différentielles hyperboliques - Solutions numériques ram Differential equations, Hyperbolic Numerical solutions Evolution equations Asymptotic theory Nichtlineare Evolutionsgleichung (DE-588)4221363-0 gnd Hyperbolische Differentialgleichung (DE-588)4131213-2 gnd |
| topic_facet | Equations d'évolution - Théorie asymptotique Equations différentielles hyperboliques - Solutions numériques Differential equations, Hyperbolic Numerical solutions Evolution equations Asymptotic theory Nichtlineare Evolutionsgleichung Hyperbolische Differentialgleichung Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006845435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008585 |
| work_keys_str_mv | AT wittingo nonlinearhyperbolicequationsindomainswithconicalpointsexistenceandregularityofsolutions |